Is x+y < 1?

[ridhamshah]

Is x+y<1?

(1) x < 8/9
(2) y < 1/8

I thought (c) but the answer is (e).

The way I solved this was x + y = 73/72 > 1, for x=8/9 and y=1/8
If x= 8/9 = 0.8888..and y=1/8 = 0.125

So if x<8/9 and y<1/8 would mean x+y = 0.88+0.124>1

[luc2r4]

Each St1 and St2 is INSUFFICIENT

Each do not give info for x +y < 1
since they provide an inequality just for one of the variables


Together {St1 and St2 } are ALSO INSUFFICIENT

Since x <8/9
y < 1/8 , Summing both inequalities : x+ y < 73/ 72

Draw a number line for x+ y < 73/ 72 and x +y < 1

Then you will see that as we found that x+ y < 73/ 72

At the interval 1 =< x+ y < 73/ 72 we can not conclude that x +y < 1

answer = E

[akhp77]

Statement 1: Insufficient
Statement 2: Insufficient

Statement 1 and 2

x + y < 73/72 = 1 + 1/72

x + y could be 1 + 1/74, 1 + 1/76, 1 + 1/200 , 1, 1/10, 1/16, 20, and so on

So we can't conclude that whether x+y would be greater than, less than, or equal to 1 but we say only that x+y < 1 + 1/72

Insufficient

Ans: E

[StaceyKoprince]

ridhamshah, I'm wondering whether your difficulty here might not have to do with how the test works (as opposed to the actual math).

They are asking a yes/no question: is x+y<1?

1) If we are given information to let us say "yes, x+y is ALWAYS less than 1" then that information is sufficient.

2) If we are given information to let us say "no, x+y is NEVER less than 1" then that information is sufficient.

3) If we are given information that tells us "sometimes x+y is less than 1 and sometimes x+y is not less than 1" then that information is insufficient.

In your example, you showed how x+y might be greater than 1. You could also choose much smaller numbers for x and y, such that the sum would be less than 1, right? In this case, we have the 3rd scenario listed above: sometimes it's less than 1 and sometimes it's not less than 1.

[anupam.global]

Is it correct to do this way?

St1 & St2)

x=LT8/9
y=LT1/8

Therefor x+y = LT8/9 +LT1/8= LT73/72

Hence it could be anything from just little over +1 OR 1 or LT +1 (positive fraction) OR any number/fraction infinetly in the negative.

Please correct me if I am wrong in my understanding. Thanks.

[tim]

sounds good to me..

[veta]

Statement 1: Insufficient
Statement 2: Insufficient

Statement 1 and 2

x + y < 73/72 = 1 + 1/72

x + y could be 1 + 1/74, 1 + 1/76, 1 + 1/200 , 1, 1/10, 1/16, 20, and so on

So we can't conclude that whether x+y would be greater than, less than, or equal to 1 but we say only that x+y < 1 + 1/72

Insufficient

Ans: E

I don't think x+y cound be 20

[jnelson0612]

Statement 1: Insufficient
Statement 2: Insufficient

Statement 1 and 2

x + y < 73/72 = 1 + 1/72

x + y could be 1 + 1/74, 1 + 1/76, 1 + 1/200 , 1, 1/10, 1/16, 20, and so on

So we can't conclude that whether x+y would be greater than, less than, or equal to 1 but we say only that x+y < 1 + 1/72

Insufficient

Ans: E

I don't think x+y cound be 20

You are right. I suspect that's a typo.

[itsmeaakash3]

Y answer is not c ?

x+ y < 73/72 which is greater than 1 .... answer is YES and so C

[jlucero]

Y answer is not c ?

x+ y < 73/72 which is greater than 1 .... answer is YES and so C

Be careful with your logic for DS. We are trying to find if x+y could be either greater than 1 or less than 1. According to:

x+y < 73/72

then x+y could be:

72.5/72 (greater than 1)

OR

71/72 (less than 1)

Two different answers means (E) we still do not have sufficient info to answer the question.

[sachin.w]

Y answer is not c ?

x+ y < 73/72 which is greater than 1 .... answer is YES and so C

Be careful with your logic for DS. We are trying to find if x+y could be either greater than 1 or less than 1. According to:

x+y < 73/72

then x+y could be:

72.5/72 (greater than 1)

OR

71/72 (less than 1)

Two different answers means (E) we still do not have sufficient info to answer the question.

I don't understand how the following can be true...

then x+y could be:71/72 (less than 1)

when we add x and y, we get 73/72.

I guess its because
x is less than 8/9 and
y is less than 1/8..
so addition can be lesser 73/72.. but still I am unable to digest this.. that it can be 71/72.. the numerator decreased and the denominator constant..

[RonPurewal]

when we add x and y, we get 73/72.

remember that these are inequalities. x and y are not actually 8/9 and 1/8; they are less than those values. more precisely, they can have any value at all that's under those respective numbers.

so addition can be lesser 73/72.. but still I am unable to digest this.. that it can be 71/72.. the numerator decreased and the denominator constant..

to prove that the statements are insufficient, you don't have to get 71/72 specifically -- you just have to get:
* a value that's less than 1 (a "yes" answer to the question)
and
* a value that's 1 or more (a "no" value to the question).

to get a "no" value, just take x and y really, really close to 8/9 and 1/8. that way, you'll get a value that's really close to 73/72.

to get a "yes" value, just take smaller numbers.
the value of 71/72 (mentioned above) can be achieved; for instance, x could be 7/8, which is less than 8/9, and y could be 1/9, which is less than 1/8 --> these values give 7/8 + 1/9 = 71/72.)
however, there's no need to shoot for a value as complicated as that. instead, you can get your "yes" answer by picking far easier values -- say, x = 0 and y = 0, to produce x + y = 0, which is certainly less than 1.

[sachin.w]

Thanks Ron. It helps.

But the following is what I need to digest:

to get a "no" value, just take x and y really, really close to 8/9 and 1/8. that way, you'll get a value that's really close to 73/72.

Problem is it is really difficult to think this way.
Any tips on how to do so would help us.
Basically, how the numbers behave under different circumstances/conditions would help us a lot.

[RonPurewal]

Problem is it is really difficult to think this way.
Any tips on how to do so would help us.
Basically, how the numbers behave under different circumstances/conditions would help us a lot.

i'm not sure what you are asking here. this is the fundamental definition of an inequality.
e.g., "less than" means any number less than a given value. so, for instance, if x < 3, then x could be, say, 2.99999999.

i think the problem is more likely to be the fractions, not the inequalities.
try replacing the 1/8 and the 8/9 with, say, 2 and 3 (so x < 2 and y < 3).
is it clear to you that, under those circumstances, x + y could be anything less than 5? like, it could be 4.99999999, etc.?

i don't know what you mean by "how the numbers behave..." -- perhaps you could explain that.

[sachin.w]

The problem was with fractions and thanks a lot for the lucid explanation!!


Regards,
Sachin